Topological phases of matter are a long-standing subject of interest in the condensed matter community, and increasingly relevant to issues in high-energy physics. Organized by: Jennifer Cano, Dominic Else, Andrey Gromov, Siddharth Parameswaran, and Yizhi You This arises because electrodynamics itself, via Maxwell's equations, can be interpreted as a structure on a U(1) fiber bundle, the so-called circle bundle.This event has been postponed due to COVID-19 and will now be held April 4 – May 27 2022. The charge conjugation symmetry is interpreted as that of electrical charge, because in all three cases (classical, quantum and geometry), one can construct Noether currents that resemble those of classical electrodynamics. In all three cases, the symmetry is ultimately revealed to be a symmetry under complex conjugation, although exactly what is being conjugated where can be at times obfuscated, depending on notation, coordinate choices and other factors. The various fundamental particles can be classified according to behavior under charge conjugation this is described in the article on C-parity.Ĭharge conjugation occurs as a symmetry in three different but closely related settings: a symmetry of the (classical, non-quantized) solutions of several notable differential equations, including the Klein–Gordon equation and the Dirac equation, a symmetry of the corresponding quantum fields, and in a general setting, a symmetry in (pseudo-) Riemannian geometry. This article focuses on exposing and articulating the C-symmetry of various important equations and theoretical systems, including the Dirac equation and the structure of quantum field theory. Earlier textbooks on cosmology, predating the 1970s, routinely suggested that perhaps distant galaxies were made entirely of anti-matter, thus maintaining a net balance of zero in the universe. It is currently believed that CP-violation during the early universe can account for the "excess" matter, although the debate is not settled. The C-symmetry is particularly troublesome, physically, as the universe is primarily filled with matter, not anti-matter, whereas the naive C-symmetry of the physical laws suggests that there should be equal amounts of both. For several decades, it appeared that the combined symmetry CP was preserved, until CP-violating interactions were discovered. An early surprise appeared in the 1950s, when Chien Shiung Wu demonstrated that the weak interaction violated P-symmetry. Unlike the continuous symmetries, the interpretation of the discrete symmetries is a bit more intellectually demanding and confusing. Verifying whether some given mathematical equation correctly models nature requires giving physical interpretation not only to continuous symmetries, such as motion in time, but also to its discrete symmetries, and then determining whether nature adheres to these symmetries. These discrete symmetries, C, P and T, are symmetries of the equations that describe the known fundamental forces of nature: electromagnetism, gravity, the strong and the weak interactions. Other important discrete symmetries are P-symmetry (parity) and T-symmetry (time reversal). The term C-symmetry is an abbreviation of the phrase "charge conjugation symmetry", and is used in discussions of the symmetry of physical laws under charge-conjugation. In physics, charge conjugation is a transformation that switches all particles with their corresponding antiparticles, thus changing the sign of all charges: not only electric charge but also the charges relevant to other forces. JSTOR ( December 2008) ( Learn how and when to remove this template message).
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